Master Thesis - Computer Graphics and Visualization - TU Delft

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E.2 Algorithm BDPT Algorithm 154 Algorithm 8 : Connect for i = 0 to NE do {Check implicit path} if i > 0 and Le (yi → yi−1) then D ← PY i + PA (yi)DY i−1 F ← FY i−1Le (yi → yi−1) w ← PY i D contribute wF along edge y0y1 end if {Connect to light path} for j = 1 to NL do if y i is visible from z j then D ← P Y i PZ j if i > 0 then PA(z j → yi) ← P−→ σ ⊥(z j → yi)G(yi ↔ z j) PA(yi−1 ← yi) ← P←− σ ⊥(yi−1 ← yi)G(yi ↔ yi−1) D ← D + PZ j PA β (z j → yi) PY i−1 + PA (yi−1 ← yi) β DY i−1 F ← F E i−1 fr (z j → y i → y i−1)G(y i ↔ z j) else F ← ˆW (z j → y 0) l2 nz j ·(y 0−z j) ρ(ny 0 ·(z j−y 0)) 3 PS (z j) end if PA(yi → z j) ← P−→ σ ⊥(yi → z j)G(yi ↔ z j) if j > 1 then PA(z j−1 ← z j) ← P←− σ ⊥(z j−1 ← z j)G(z j ↔ z j−1) D ← D + PY i PA β (yi → z j) PZ j−1 + PA (z j−1 ← z j) β DZ j−1 F ← F · FL j−1 fr (z j+1 → z j → yi) else D ← D + PY i PA (yi → z1) β F ← F · Le (z1 → yi) end if w ← PY i PZ j D if i = 0 then contribute wF along edge y 0z j else contribute wF along edge y 0y 1 end if end if end for end for
Appendix F MLT Mutations This appendix gives a detailed description of the lens and caustic mutations in the MLT algorithm as discussed in section 2.9. Remember that the MLT algorithm generates a sequence of light transport paths through mutations. A mutation transforms a path X into a new path Y by making small changes to the original path. Two important mutation strategies are the lens and caustic mutation. Both mutation strategies mutate the first m + 1 path vertices on a path X = x0 ···xk into y0 ···ym to form the mutated path Y = y0 ···ymxm+1 ···xk. The lens mutation starts from the eye and mutates the vertices through forward sampling. The caustic mutation starts somewhere on the path and mutating backwards towards the eye (for the caustic mutation, m < k). Both mutations preserve the path length (See section 2.9 for more details on the mutation strategies). In this appendix, we will show how to compute the acceptance probability for the lens and caustic mutation strategies and show the algorithms for generating such mutations in pseudo code. F.1 Acceptance probability Remember from section 2.8 that for some path Y that is generated from path X through mutations, the acceptance probability in the MLT algorithm is defined as a = min 1, f (Y) p(X|Y) f (X) p(Y|X) (F.1) Because usually only a part of the path is mutated, many of the factors in this equation cancel out. f (Y) Lets start with the measurement contribution factor f (X) in the acceptance probability. When 0 < m < k, that is, only the first m+1 vertices on the path are mutated and the remaining vertices xm+1 ···xk = ym+1 ···yk stay the same, some of the factors in both measurement contribution functions cancel out, resulting in f (y0 ···yk) f (x0 ···xk) = Wi (y1 → y0) Wi (x1 → x0) m ∏ j=0 G(y j ↔ y j+1) G(x j ↔ x j+1) m+1 ∏ j=1 fr (y j+1 → y j → y j−1) fr (x j+1 → x j → x j−1) (F.2) 155
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Unbiased physically based rendering
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c○ 2010 Dietger van Antwerpen. Co
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ii memory-footprint independent of
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Contents Preface iii Contents v Lis
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CONTENTS CONTENTS Bibliography 131
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List of Figures List of Figures x 7
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List of Tables 5.1 Test scenes . .
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Chapter 1 Introduction Since the in
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Introduction 1.1 Summary of Contrib
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Part I Preliminaries 5
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2.1 Rendering equation Unbiased Ren
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2.3 Unbiased Monte Carlo estimate U
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2.5 Importance sampling Unbiased Re
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2.7 BiDirectional Path Tracing Unbi
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2.7 BiDirectional Path Tracing Unbi
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2.9 Metropolis Light Transport Unbi
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2.9 Metropolis Light Transport Unbi
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2.10 Energy Redistribution Path Tra
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Chapter 3 3.1 Introduction GPGPU Mo
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GPGPU 3.3 Memory Hierarchy divergin
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GPGPU 3.3 Memory Hierarchy (1 trans
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GPGPU 3.5 Parallel scan Algorithm 3
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4.1 GPU ray tracing Related Work 34
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4.2 Unbiased rendering Related Work
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Chapter 5 The Problem Statement In
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The Problem Statement 5.1 Related w
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Chapter 6 6.1 Introduction Hybrid T
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Hybrid Tracer 6.2 Hybrid architectu
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Hybrid Tracer 6.3 Results 6.3.2 Hyb
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Hybrid Tracer 6.3 Results 6.3.3 Con
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7.2 Two-Phase PT Path Tracer (PT) 5
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7.4 Stream compaction Path Tracer (
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7.4 Stream compaction Path Tracer (
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7.5 Results Path Tracer (PT) 58 sam
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7.5 Results Path Tracer (PT) most g
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7.5 Results Path Tracer (PT) 62 Mil
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7.5 Results Path Tracer (PT) 64 Mil
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Chapter 8 Streaming BiDirectional P
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Streaming BiDirectional Path Tracer
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9.2 ERPT mutation Energy Redistribu
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Master Thesis - Computer Graphics and Visualization - TU Delft

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